Liquid Propellant Primer

When somebody online asks the question “what’s the best liquid rocket propellant mix”, you are bound to hear a preposterous amount of b*llshit flying as everybody tries to champion their favorite mix, refusing to heed the opposition’s remarks.

“It’s Hydrolox without a doubt”, says a boring square who really never got over STS, “look at that absolute unit of a specific impulse.”.

“Nothing holds a candle to Methalox”, says a pimply-faced kid who does unspeakable things at night with a picture of a certain African-American billionaire, “it’s the hottest sh*t going around today, and it’s also really damn cheap.”.

“Bollocks”, says a man who was already old when Gagarin went up, “what you really need is density impulse, and Kerolox’ll give you that.”.

“You’re all wrong”, says yet another figure in a thick Russian accent, trailing ice crystals and the smell of cheap vodka, “look no further than Hypergolics, good specific and density impulses, and they’re really easy to work with.”.

At this point the situation starts degenerating pretty badly, and it won’t take long before you have Hugo Boss-wearing vegetarians proposing Ethanol in liquid Oxygen just because the Germans did, or somebody asking you to dilute liquid Fluorine in your Oxygen, just try it, and some utter lunatic asking you to run a dynamic-mixture Kero-Hydro-Lox tripropellant rocket like the people in old country did when vodka was cheap and communism plenty and, by the time some smart-ass mentions the yanks actually fired a rocket burning Lithium in Fluorine and then added Hydrogen until satisfied, back when the cocaine rained like snow in the offices of Rocketdyne, I am about to get an actual unironic aneurysm.

The reality is that the question itself is terribly flawed - there is no all-around best liquid rocket propellant mix; rather, you have several mixes with different strengths and weaknesses, and an important part of designing your very own rocket is to choose the mix that works better for your use case.

Measures of merit for rocket propellants

Broadly speaking, one can pinpoint four main measures of merit in the choice of a liquid rocket propellant mix:

1. Specific Impulse
2. Density Impulse
3. Handling Concerns
4. Cost

The first one, specific impulse, simply refers to how much a kilogram of mix can kick you downrange - an extremely important parameter for a very simple reason: the rocket equation shows how the final velocity change of your rocket depends linearly on your specific impulse and logarithmically on your mass ratio, so doubling your specific impulse doubles the total velocity change you can make while doubling your mass ratio not so much.

The second one, density impulse, is merely specific impulse times the specific gravity of the propellant mixture, and is an extremely underrated measure of merit as far as rocket propellants in popular knowledge are concerned: propellant tanks, unfortunately, are not massless nor of negligible drag and, being stuck with a low density-impulse propellant, you risk ending up in a situation where you just can’t achieve the mass ratio you need for your mission because the tanks cut so much into your payload margin it ends up being negative. On the other hand, a high density-impulse propellant can stick a lot of gas into the same tank, allowing you to get some embarrassing mass ratios in a nice slender rocket and partly offsetting a lower specific impulse it may have.

The third one, handling concerns, is a fuzzy category that groups together all those little issues that may crop in the design and operation of an actual rocket vehicle: does your propellant need an external ignition system, or is it a nice, easy hypergol? Is your propellant mix storable, or are you using cryogenic rocket propellants? Can your fuel or oxidizer be used to cool the engine bell, or will you have to find another solution? Are your fuel and oxidizer generally inoffensive chemicals, or will you need special precautions when handling them? All these questions, and many more, sketch you a general concept of how the rocket will be operated and the complexity of such an endeavor.

The last measure of merit is, of course, cost - how much bang for your buck you get. Large rockets and small rockets procured in large numbers and/or flown many times can rapidly burn outrageous amounts of chemicals and thus even a very small cost saving in mixture choice can end up saving quite a bit of money in the long run. While most rocket propellants are too cheap to matter, some of the exotic high-performance mixes can get unaffordable.

As a final note, it is important to remember that the measures of merit given above are not given in order of importance; instead, their relative importance depends heavily on the use case of the rocket in question: a tactical rocket system will heavily prioritize measures 2 and 3 above anything else, while a launch vehicle will prioritize measures 1 and 2, with 3 and 4 being given secondary importance and, even within the launch vehicle example, you will have a lower stage prioritizing 2 above all while the upper stage stresses 1 more and so on and so forth.

Additionally, your mixture choice may be conditioned by external factors such as availability, political/logistical/health, and safety choices - as an example, while the US Army and US Air Force operated many storable hypergolic rocket propulsion systems in their history, the US Navy was always wary of them due to fear of fires aboard ships.

Fuels and Oxidizers and Exhaust oh my

The reaction happening within a bipropellant rocket engine is naught but a simple redox one - the oxidizer, well, duh, oxidizing the fuel, a lot of chemical bonds being broken and their energy heating up the resulting compound(s) until they become rather hot gases and get blasted outta the rocket’s tailpipe. A good grasp of the chemistry being involved here goes most of the way of getting a bearing on the already-mentioned measures of merit.

First of all, let’s talk about what we want from a rocket propellant mix to get a high specific impulse.

An absolute conservation-of-energy-dictated upper bound on the exhaust velocity (and therefore specific impulse) of a chemical rocket propellant combination can be given by this simple equation:

$V_{eMAX}={\sqrt {2E_{s}}}$

• where $V_{eMAX}$ is the exhaust velocity.
• where $E_{s}$ is the specific energy of the propellant mixture.

However, this is far from the whole game. To make good use of the propellant’s specific energy, the exhaust’s average molar mass must be as low as possible. This is because, assuming perfect expansion, the equation for a rocket’s exhaust velocity is:

$V_{e}={\sqrt {{\frac {2k}{k-1}}\cdot {\frac {R}{M}}\cdot E_{s}\cdot C_{p}}}$

• Where $k$ is the heat capacity ratio.
• Where $R$ is the ideal gas constant.
• Where $M$ is the exhaust’s average molar mass.
• Where $C_{p}$ is the exhaust’s specific heat.

Thus, broadly speaking to achieve higher exhaust velocities, one must seek a propellant combination with very high specific energies while at the same time avoiding ones with exhaust average molar masses that are too high. Matters of specific heat and heat capacity ratio of the exhaust additionally ensure that the business will never be boring and there will be gnarly choices to make.

The first part of a fuel/oxidizer combination is, of course, the fuel. God is merciful, and He has given us a bountiful amount of cool things that can be burnt in a rocket motor: first of all, we have the Hydrogen of great promise, then the many Hydrocarbons, the always-enchanting Hydrazines as well as a wealth of minor contenders, such as Alcohols and so on and so forth.

It must be, however, noted that certain propellants and oxidizers are liquid at different temperature ranges, some are liquid at room temperature, some are liquid at 200 degrees Celsius below freezing and are referred to as soft cryogens, and the hard cryogens are even colder with some liquid only barely above absolute zero.

Hydrogen boasts a very high specific energy with basically anything that can burn it, as well as such a low molecular mass that even a slight excess of hydrogen in the propellant mix will ensure very low molecular mass in the exhaust, but it suffers from a pitifully low density that gravely hurts the impulse density of any combination using it. It is also a hard cryogen, requiring very low temperatures for storage. However, it also has a tremendous heat capacity, making it very useful for any engines which need cooling or for using some kind of transpiration heating. Hydrogen is a true primadonna - it can give you much, but it also asks much in return.

Hydrocarbons, on the other hand, are a large family of fuels that, as a rule, are extremely pedestrian. Some, like Methane, are soft cryogens while others, like Kerosene, are liquid at room temperature, but all are thankfully boring molecules that will not expend undue energy to kill you if you avoid giving them a reason to, a true rarity in rocketry. In fact, you could go drinking rocket-grade Kerosene and live to tell the tale, although I guess that a big part of your tale would be about how sh*t it tastes. Hydrocarbons in general offer lower specific impulses than Hydrogen but, unlike Hydrogen, they have densities that are not utterly awful. As a rule, smaller Hydrocarbons, such as Methane, offer higher specific impulses but lower densities, while heavier ones, such as Kerosene, offer higher densities but lower specific impulses. There is really not much else to say about Hydrocarbons: they give exactly what they promise, not a bit more, not a bit less, and that’s good.

Alcohols are a bit like Hydrocarbons, except somehow even more boring and with a pleasantly low combustion temperature for their specific impulse, combined with high specific heat, meaning that cooling Alcohol-fired engines is generally a cakewalk. However, their very boringness starts to hurt them in this case, as they have lower performance than Hydrocarbons without gaining much in exchange. However, it bears noting that the heaviest Alcohols, such as Isopropyl Alcohol, have performances broadly comparable to heavy Hydrocarbons, such as Kerosene, making them somewhat competitive if external factors make them easier to procure.

Hydrazines, instead, are a family of chemical compounds that have a bit of a reputation in popular discourse, mostly due to the fact that they have weird-ass names such as, well, Hydrazine, Monomethylhydrazine, Unsymmetrical Dimethylhydrazine, and the like and probably also due to the fact that they are, depending on the time of the day and phase of the Moon, toxic, corrosive, explosive and known to cause cancer to the State of California. On the other hand, Hydrazines give specific impulses only slightly lower than Hydrocarbons, but at even higher densities, are easily storable and hypergolic with basically anything you care to burn them with. This makes them competitive with other fuels in situations where performance and responsiveness are more important than environmental impact statements.

Additionally, we also have some exotics to work with, such as Boranes, Silanes and the like but, although the performance they promise is high, wringing it out has proved to be a not so small problem and dealing with them is a pain and half, so we can easily ignore them for the purpose of this primer.

We are instead much less lucky as far as oxidizers are concerned. Broadly speaking, our choice is limited to Oxygen, Nitrous Oxide, Hydrogen Peroxide, Nitric Acid, Dinitrogen Tetroxide, and Fluorine (which also come in various fluorine-containing chemicals in an attempt to mitigate its worst features).

Oxygen, in its liquid form, is a dense soft cryogen that has ended up being sort of the natural oxidizer choice when storability is not a pressing need. It gives high performance and, while it likes to turn stuff it soaks into high explosives, it is also pretty safe when handled with a bit of seriousness. Getting splashed with it is still bad, but you shouldn’t get splashed with rocket oxidizers anyway.

Nitrous Oxide is essentially a rather Rube Goldberg-ish way of bringing Oxygen to the combustion chamber, but it allows you to do away with cryogenic storage, paying for that with a sizable performance hit, risk of explosions, and lower density. All of this means that nowadays Nitrous Oxide is used mostly for hobby purposes.

Hydrogen Peroxide is, in the words of John Clark of Ignition! fame, the eternal bridesmaid. It has a lot to recommend it, as it's dense, storable at room temperatures, and doesn't suffer too badly in performance in comparison with straight liquid Oxygen. However, this isn't the stuff you'd buy at the drug store. You can't just go buy a bottle of disinfectant and hope to launch your moon rocket - drugstore hydrogen peroxide is typically only a few percent actually Hydrogen Peroxide, with the rest being plain old water. The limits available for solvent use through many chemical suppliers are still only 50-60% Hydrogen Peroxide, and thus almost half water. Moon rockets need much higher purity, north of 80 or 90%. At these levels, it's known as "High-Test Peroxide" (HTP), which can cause burns to skin, set things on fire, and decompose spontaneously given a catalyst (useful for hypergolic performance, but troublesome for cleaning). This HTP is thus also a rather touchy chemical, requiring great attention to materials choice when building the engine and tanks and great cleanliness when maintaining and refueling them if one wants to store good old Peroxide without explosions.

Nitric Acid and Dinitrogen Tetroxide are the oxidizers of choice to be employed with Hydrazines: relatively dense, giving performance pretty close to liquid Oxygen and easily storable, they are however nearly as noxious, if not more than the Hydrazines themselves.

Lastly, there is Fluorine - Fluorine is an utterly vile chemical, but its comical electronegativity means that any redox reaction it is involved in is bound to be spicy, and so rocket engineers of yore enlisted this horrible thing in the unending fight to wring out a few more seconds of specific impulse from existing fuels. Liquid Fluorine, when burned with Hydrogen-rich fuels, is essentially a better liquid Oxygen. Additionally, Fluorine is hypergolic with most things, which is good, but also sometimes with the engine itself, which is not. Offering high performance at perhaps too huge of a bother, Fluorine has, as of now, remained a feature more of napkin designs and studies and sometimes even of actual test articles, but never of operational rocket systems. As the last twist, you can mix a bit of fluorine into your liquid oxygen, getting a performance boost of ten seconds or so, without having to deal with most of the hassle that comes with fluorine.

The Great Propellant Mix Table

Fuel	Oxidizer	O/F	Specific Gravity	Specific Impulse (Sea Level Adapted Nozzle)	Density Impulse (Sea Level Adapted Nozzle)	Specific Impulse (Vacuum Level Adapted Nozzle)	Density Impulse (Vacuum Level Adapted Nozzle)
Hydrogen	Oxygen	4.8	0.33	422	139	482	159
Hydrogen	Fluorine	12	0.61	447	272	507	309
Methane	Oxygen	3.5	0.92	342	314	402	369
Methane	Fluorine	4.7	1.1	383	421	447	491
Kerosene	Oxygen	2.8	1.16	333	386	391	453
Kerosene	Nitrous Oxide	9.3	1.16	284	329	299	346
Hydrazine	Nitric Acid	1.6	1.26	303	381	345	434
Hydrazine	Dinitrogen Tetroxide	1.4	1.21	319	385	365	441
Hydrazine	Fluorine	2.4	1.48	401	593	455	673
MMH	Nitric Acid	2.7	1.26	300	378	345	434
MMH	Dinitrogen Tetroxide	2.2	1.16	316	366	367	425
UDMH	Nitric Acid	3.3	1.24	298	369	344	427
UDMH	Dinitrogen Tetroxide	2.7	1.18	314	370	366	431

Note: this table is far from an exhaustive list of all possible propellant combinations, but rather it is a simple panorama to give the reader an idea of the trends and rough quantities involved in the choice of a rocket propellant mix depending on the mission. It is additionally worth remembering that, in some cases, one may choose a different mixture ratio than the optimal one for reasons such as higher density allowing higher volumetric impulses.

Historical Notes

Hydrogen/Oxygen

High specific impulse combination popular for upper stages and at times employed even in first stages, as in Ariane 5’s EPC motors. Oxygen is a soft cryogen, Hydrogen is a hard cryogen. Not hypergolic.

Hydrogen/Fluorine

Experimental high-performance combination designed for upper stages. Test-fired but never flown. Hydrogen is a hard cryogen, Fluorine is a soft one. Additionally, liquid Fluorine has serious safety and handling issues. Hypergolic.

Methane/Oxygen

Used in several modern launch vehicles, delivers slightly higher specific impulse than Kerosene/Oxygen, but has a lower average density. Both components are soft cryogens. Not hypergolic.

Methane/Fluorine

Theoretical combination for upper stage work. Methane and Fluorine are both soft cryogens. Hypergolic, high impulse density, and specific impulse.

Kerosene/Oxygen

Workhorse combination that is popular with older launch vehicles and first-generation intercontinental ballistic missiles. Easy to handle and to work with, Kerosene is storable while Oxygen is a soft cryogen. Good specific impulse and impulse density values. Not hypergolic.

Kerosene/Nitrous Oxide

Hobby rocket combination, easy to handle, both components are storable. Middling performance. Not hypergolic.

Credit

• To David Black for writing the article
• To Rocketguy for minor edits
• To Tshhmon for minor edits